dot(a: any, b: any) → number

sub(a: any, b: any) → any

closestAxisParam(ro: any, rd: any, ao: any, ad: any) → number

Parameter `s` along axis (ao + s*ad) at the point closest to the ray (ro + t*rd). `rd` and `ad` need not be unit length. Returns 0 for a degenerate (parallel) configuration.

rayPlane(ro: any, rd: any, planePoint: any, n: any) → any

Intersection point of ray (ro + t*rd, t>=0) with the plane through `planePoint` with normal `n`. Returns nil if parallel or behind the origin.

snap(v: number, inc: number) → number

Quantize `v` to the nearest multiple of `inc`. `inc <= 0` returns `v`.

worldPerPixel(dist: number, fovY: number, viewportH: number) → number

World units spanned by one screen pixel at `dist` from the camera, for a vertical FOV `fovY` (radians) and viewport height `viewportH` px. Used to keep handles a roughly constant on-screen size: handleLen = pixels * worldPerPixel.

rotateAround(point: any, pivot: any, axis: any, angle: number) → any

Rotate `point` around `pivot` by `angle` (radians) about unit-ish `axis` (normalized internally). Right-handed. Returns the new { x, y, z }.

scaleAround(point: any, pivot: any, factors: any) → any

Scale `point`'s offset from `pivot` component-wise by `factors`.

axisAngleQuat(axis: any, angle: number) → any

Unit quaternion { x, y, z, w } for a rotation of `angle` radians about `axis` (normalized internally). A degenerate axis yields identity.

rotateVec(q: any, vec: any) → any

`vec` rotated by unit quaternion `q` ({ x, y, z, w }): the rotated-basis expansion of `q v q⁻¹`, so a frame's unit axes carried through an entity's world rotation come out as that entity's own axes.

quatMul(a: any, b: any) → any

Hamilton product `a * b` (apply `b` first, then `a`). Composing a world-space delta rotation `d` onto a start rotation `q0` is `quatMul(d, q0)`.

projectOntoPlane(vec: any, n: any) → any

Component of `vec` (a world offset) that lies within the plane whose unit normal is `n`: `vec - (vec·n) n`. Used to keep a planar drag on its plane.